Stoats (Mustela erminea) were removed from three islands in Fiordland with traps at densities of one trap per 3.6–11 ha to determine whether stoats could be eradicated with traps at these densities, and how long eradication might take. Stoats were successfully eradicated from the two of the three islands within 4 months of the start of trapping. In a separate experiment, stoat traps were also set and checked for 4 years on 19 small islands at varying distances offshore, and the relationship between the number of stoats caught, the distance offshore and the length of adjacent mainland coast documented. From these data, we estimated the likely rate of stoat re-invasion onto large islands in Fiordland such as Resolution, Secretary and Coal, which are candidates for future stoat eradication programmes. We conclude that permanent trapping networks on large islands could keep stoat numbers at levels low enough to allow the recovery or re-introduction of endangered wildlife.